Firing rate optimization of cyclic timed event graphs by token allocations

In this paper, we deal with the problem of allocating a given number of tokens in a cyclic timed event graph (CTEG) so as to maximize the firing rate of the net. We propose three different approaches. The first one is a "greedy" incremental procedure that is computationally very efficient. The only drawback is that the convergence to the optimum is guaranteed only when the set of places where tokens can be allocated satisfies given constraints. The other two procedures involve the solution of a mixed integer linear programming problem. The first one needs the knowledge of the elementary circuits, thus it is convenient only for those classes of CTEG whose number of elementary circuits is roughly equal to the number of places, such as some kanban-systems. On the contrary, the second one enables one to overcome this difficulty, thus providing an efficient tool for the solution of allocation problems in complex manufacturing systems like job-shop systems

Performance Bounds for Synchronized Queueing Networks

Las redes de Petri estocásticas constituyen un modelo unificado de las diferentes extensiones de redes de colas con sincronizaciones existentes en la literatura, válido para el diseño y análisis de prestaciones de sistemas informáticos distribuidos. En este trabajo se proponen técnicas de cálculo de cotas superiores e inferiores de las prestaciones de redes de Petri estocásticas en estado estacionario. Las cotas obtenidas son calculables en tiempo polinómico en el tamaño del modelo, por medio de la resolución de ciertos problemas de programación lineal definidos a partir de la matriz de incidencia de la red (en este sentido, las técnicas desarrolladas pueden considerarse estructurales). Las cotas calculadas dependen sólamente de los valores medios de las variables aleatorias que describen la temporización del sistema, y son independientes de los momentos de mayor orden. Esta independencia de la forma de las distribuciones de probabilidad asociadas puede considerarse como una útil generalización de otros resultados existentes para distribuciones particulares, puesto que los momentos de orden superior son, habitualmente, desconocidos en la realidad y difíciles de estimar. Finalmente, las técnicas desarrolladas se aplican al análisis de diferentes ejemplos tomados de la literatura sobre sistemas informáticos distribuidos y sistemas de fabricación. ******* Product form queueing networks have long been used for the performance evaluation of computer systems. Their success has been due to their capability of naturally expressing sharing of resources and queueing, that are typical situations of traditional computer systems, as well as to their efficient solution algorithms, of polynomial complexity on the size of the model. Unfortunately, the introduction of synchronization constraints usually destroys the product form solution, so that general concurrent and distributed systems are not easily studied with this class of models. Petri nets have been proved specially adequate to model parallel and distributed systems. Moreover, they have a well-founded theory of analysis that allows to investigate a great number of qualitative properties of the system. In the original definition, Petri nets did not include the notion of time, and tried to model only the logical behaviour of systems by describing the causal relations existing among events. This approach showed its power in the specification and analysis of concurrent systems in a way independent of the concept of time. Nevertheless the introduction of a timing specification is essential if we want to use this class of models for the performance evaluation of distributed systems. One of the main problems in the actual use of timed and stochastic Petri net models for the quantitative evaluation of large systems is the explosion of the computational complexity of the analysis algorithms. In general, exact performance results are obtained from the numerical solution of a continuous time Markov chain, whose dimension is given by the size of the state space of the model. Structural computation of exact performance measures has been possible for some subclasses of nets such as those with state machine topology. These nets, under certain assumptions on the stochastic interpretation are isomorphic to Gordon and Newell's networks, in queueing theory terminology. In the general case, efficient methods for the derivation of performance measures are still needed. Two complementary approaches to the derivation of exact measures for the analysis of distributed systems are the utilization of approximation techniques and the computation of bounds. Approximate values for the performance parameters are in general more efficiently derived than the exact ones. On the other hand, "exactness" only exists in theory! In other words, numerical algorithms must be applied in practice for the computation of exact values, therefore making errors is inevitable. Performance bounds are useful in the preliminary phases of the design of a system, in which many parameters are not known accurately. Several alternatives for those parameters should be quickly evaluated, and rejected those that are clearly bad. Exact (and even approximate) solutions would be computationally very expensive. Bounds become useful in these instances since they usually require much less computation effort. The computation of upper and lower bounds for the steady-state performance of timed and stochastic Petri nets is considered in this work. In particular, we study the throughput of transitions, defined as the average number of firings per time unit. For this measure we try to compute upper and lower bounds in polynomial time on the size of the net model, by means of proper linear programming problems defined from the incidence matrix of the net (in this sense, we develop structural techniques). These bounds depend only on the mean values and not on the higher moments of the probability distribution functions of the random variables that describe the timing of the system. The independence of the probability distributions can be viewed as a useful generalization of the performance results, since higher moments of the delays are usually unknown for real cases, and difficult to estimate and assess. From a different perspective, the obtained results can be applied to the analysis of queueing networks extended with some synchronization schemes. Monoclass queueing networks can be mapped on stochastic Petri nets. On the other hand, stochastic Petri nets can be interpreted as monoclass queueing networks augmented with synchronization primitives. Concerning the presentation of this manuscript, it should be mentioned that chapter 1 has been written with the object of giving the reader an outline of the stochastic Petri net model: its definition, terminology, basic properties, and related concepts, together with its deep relation with other classic stochastic network models. Chapter 2 is devoted to the presentation of the net subclasses considered in the rest of the work. The classification presented here is quite different from the one which is usual in the framework of Petri nets. The reason lies on the fact that our classification criterion, the computability of visit ratios for transitions, is introduced for the first time in the field of stochastic Petri nets in this work. The significance of that criterion is based on the important role that the visit ratios play in the computation of upper and lower bounds for the performance of the models. Nevertheless, classical important net subclasses are identified here in terms of the computability of their visit ratios from different parameters of the model. Chapter 3 is concerned with the computation of reachable upper and lower bounds for the most restrictive subclass of those presented in chapter 2: marked graphs. The explanation of this fact is easy to understand. The more simple is the model the more accessible will be the techniques an ideas for the development of good results. Chapter 4 provides a generalization for live and bounded free choice nets of the results presented in the previous chapter. Quality of obtained bounds is similar to that for strongly connected marked graphs: throughput lower bounds are reachable for bounded nets while upper bounds are reachable for 1-bounded nets. Chapter 5 considers the extension to other net subclasses, like mono-T-semiflow nets, FRT-nets, totally open deterministic systems of sequential processes, and persistent nets. The results are of diverse colours. For mono-T-semiflow nets and, therefore, for general FRT-nets, it is not possible (so far) to obtain reachable throughput bounds. On the other hand, for bounded ordinary persistent nets, tight throughput upper bounds are derived. Moreover, in the case of totally open deterministic systems of sequential processes the exact steady-state performance measures can be computed in polynomial time on the net size. In chapter 6 bounds for other interesting performance measures are derived from throughput bounds and from classical queueing theory laws. After that, we explore the introduction of more information from the probability distribution functions of service times in order to improve the bounds. In particular, for Coxian service delay of transitions it is possible to improve the throughput upper bounds of previous chapters which held for more general forms of distribution functions. This improvement shows to be specially fruitful for live and bounded free choice nets. Chapter 7 is devoted to case studies. Several examples taken from literature in the fields of distributed computing systems and manufacturing systems are modelled by means of stochastic Petri nets and evaluated using the techniques developed in previous chapters. Finally, some concluding remarks and considerations on possible extensions of the work are presented

Elasticity and Petri nets

Digital electronic systems typically use synchronous clocks and primarily assume fixed duration of their operations to simplify the design process. Time elastic systems can be constructed either by replacing the clock with communication handshakes (asynchronous version) or by augmenting the clock with a synchronous version of a handshake (synchronous version). Time elastic systems can tolerate static and dynamic changes in delays (asynchronous case) or latencies (synchronous case) of operations that can be used for modularity, ease of reuse and better power-delay trade-off. This paper describes methods for the modeling, performance analysis and optimization of elastic systems using Marked Graphs and their extensions capable of describing behavior with early evaluation. The paper uses synchronous elastic systems (aka latency-tolerant systems) for illustrating the use of Petri nets, however, most of the methods can be applied without changes (except changing the delay model associated with events of the system) to asynchronous elastic systems.Peer ReviewedPostprint (author's final draft

Exploring resource/performance trade-offs for streaming applications on embedded multiprocessors

Embedded system design is challenged by the gap between the ever-increasing customer demands and the limited resource budgets. The tough competition demands ever-shortening time-to-market and product lifecycles. To solve or, at least to alleviate, the aforementioned issues, designers and manufacturers need model-based quantitative analysis techniques for early design-space exploration to study trade-offs of different implementation candidates. Moreover, modern embedded applications, especially the streaming applications addressed in this thesis, face more and more dynamic input contents, and the platforms that they are running on are more flexible and allow runtime configuration. Quantitative analysis techniques for embedded system design have to be able to handle such dynamic adaptable systems. This thesis has the following contributions: - A resource-aware extension to the Synchronous Dataflow (SDF) model of computation. - Trade-off analysis techniques, both in the time-domain and in the iterationdomain (i.e., on an SDF iteration basis), with support for resource sharing. - Bottleneck-driven design-space exploration techniques for resource-aware SDF. - A game-theoretic approach to controller synthesis, guaranteeing performance under dynamic input. As a first contribution, we propose a new model, as an extension of static synchronous dataflow graphs (SDF) that allows the explicit modeling of resources with consistency checking. The model is called resource-aware SDF (RASDF). The extension enables us to investigate resource sharing and to explore different scheduling options (ways to allocate the resources to the different tasks) using state-space exploration techniques. Consistent SDF and RASDF graphs have the property that an execution occurs in so-called iterations. An iteration typically corresponds to the processing of a meaningful piece of data, and it returns the graph to its initial state. On multiprocessor platforms, iterations may be executed in a pipelined fashion, which makes performance analysis challenging. As the second contribution, this thesis develops trade-off analysis techniques for RASDF, both in the time-domain and in the iteration-domain (i.e., on an SDF iteration basis), to dimension resources on platforms. The time-domain analysis allows interleaving of different iterations, but the size of the explored state space grows quickly. The iteration-based technique trades the potential of interleaving of iterations for a compact size of the iteration state space. An efficient bottleneck-driven designspace exploration technique for streaming applications, the third main contribution in this thesis, is derived from analysis of the critical cycle of the state space, to reveal bottleneck resources that are limiting the throughput. All techniques are based on state-based exploration. They enable system designers to tailor their platform to the required applications, based on their own specific performance requirements. Pruning techniques for efficient exploration of the state space have been developed. Pareto dominance in terms of performance and resource usage is used for exact pruning, and approximation techniques are used for heuristic pruning. Finally, the thesis investigates dynamic scheduling techniques to respond to dynamic changes in input streams. The fourth contribution in this thesis is a game-theoretic approach to tackle controller synthesis to select the appropriate schedules in response to dynamic inputs from the environment. The approach transforms the explored iteration state space of a scenario- and resource-aware SDF (SARA SDF) graph to a bipartite game graph, and maps the controller synthesis problem to the problem of finding a winning positional strategy in a classical mean payoff game. A winning strategy of the game can be used to synthesize the controller of schedules for the system that is guaranteed to satisfy the throughput requirement given by the designer

On Minimum-time Control of Continuous Petri nets: Centralized and Decentralized Perspectives

Muchos sistemas artificiales, como los sistemas de manufactura, de logística, de telecomunicaciones o de tráfico, pueden ser vistos "de manera natural" como Sistemas Dinámicos de Eventos Discretos (DEDS). Desafortunadamente, cuando tienen grandes poblaciones, estos sistemas pueden sufrir del clásico problema de la explosión de estados. Con la intención de evitar este problema, se pueden aplicar técnicas de fluidificación, obteniendo una relajación fluida del modelo original discreto. Las redes de Petri continuas (CPNs) son una aproximación fluida de las redes de Petri discretas, un conocido formalismo para los DEDS. Una ventaja clave del empleo de las CPNs es que, a menudo, llevan a una substancial reducción del coste computacional. Esta tesis se centra en el control de Redes de Petri continuas temporizadas (TCPNs), donde las transiciones tienen una interpretación temporal asociada. Se asume que los sistemas siguen una semántica de servidores infinitos (velocidad variable) y que las acciones de control aplicables son la disminución de la velocidad del disparo de las transiciones. Se consideran dos interesantes problemas de control en esta tesis: 1) control del marcado objetivo, donde el objetivo es conducir el sistema (tan rápido como sea posible) desde un estado inicial a un estado final deseado, y es similar al problema de control set-point para cualquier sistema de estado continuo; 2) control del flujo óptimo, donde el objetivo es conducir el sistema a un flujo óptimo sin conocimiento a priori del estado final. En particular, estamos interesados en alcanzar el flujo máximo tan rápido como sea posible, lo cual suele ser deseable en la mayoría de sistemas prácticos. El problema de control del marcado objetivo se considera desde las perspectivas centralizada y descentralizada. Proponemos varios controladores centralizados en tiempo mínimo, y todos ellos están basados en una estrategia ON/OFF. Para algunas subclases, como las redes Choice-Free (CF), se garantiza la evolución en tiempo mínimo; mientras que para redes generales, los controladores propuestos son heurísticos. Respecto del problema de control descentralizado, proponemos en primer lugar un controlador descentralizado en tiempo mínimo para redes CF. Para redes generales, proponemos una aproximación distribuida del método Model Predictive Control (MPC); sin embargo en este método no se considera evolución en tiempo mínimo. El problema de control de flujo óptimo (en nuestro caso, flujo máximo) en tiempo mínimo se considera para redes CF. Proponemos un algoritmo heurístico en el que calculamos los "mejores" firing count vectors que llevan al sistema al flujo máximo, y aplicamos una estrategia de disparo ON/OFF. También demostramos que, debido a que las redes CF son persistentes, podemos reducir el tiempo que tarda en alcanzar el flujo máximo con algunos disparos adicionales. Los métodos de control propuestos se han implementado e integrado en una herramienta para Redes de Petri híbridas basada en Matlab, llamada SimHPN

On the Performance Estimation and Resource Optimisation in Process Petri Nets

Many artificial systems can be modeled as discrete dynamic systems in which resources are shared among different tasks. The performance of such systems, which is usually a system requirement, heavily relies on the number and distribution of such resources. The goal of this paper is twofold: first, to design a technique to estimate the steady-state performance of a given system with shared resources, and second, to propose a heuristic strategy to distribute shared resources so that the system performance is enhanced as much as possible. The systems under consideration are assumed to be large systems, such as service-oriented architecture (SOA) systems, and modeled by a particular class of Petri nets (PNs) called process PNs. In order to avoid the state explosion problem inherent to discrete models, the proposed techniques make intensive use of linear programming (LP) problems

Modeling and simulation of healthcare pharmaceutical environments: a Petri nets approach

This study examines the drug distribution procedure in hospital, based on a bibliographic research and an interview with the pharmacy director of “Hospital de l Rio Ortega” in Vallado lid, Spain. It was necessary to elaborate a theoretical flux-gram of the medication distribution procedure describing the various stages in the process, as well as the objectives of the system, and its critical issues. All these steps depend on various health care providers and health care assistants directly linked. This systemization allowed the observance of the critical knots, understood as the processes and elements with critical impact over the quality of the distribution system. The understandi ng of the possible causes of the system‟s problems serves here as the basis for the formulation issues that make the evaluation possible. There are two basic known types of drug distribution systems: collective and individual. The collective system is the most primitive, although there are hospitals worldwide that adopt this system, considered to be the simplest and lowest in cost of deployment. The individual distribution system is more complex, it needs more professional pharmacists and a hospital pharmacy working around the clock and has as main features the fact that the product or drug is dispensed per patient, and not for the sector in which one may find himself hospitalized. The research of medication errors due to the type of distribution system adopted by hospitals has created a debate on the advantages and disadvantages of the existing systems. The use of a system model for distribution of medicines will provide a more appropriate reduction in risk of errors and foremost a reduction in hospital costs. One objective of this study is to show the best method of distribution of medicines in a hospital pharmacy, that is, the method of distribution in which the chance to experience a medication error would be smaller, and distribution times as well as staff needs were reduced to a minimum. The main objective of this work is to model the medication distribution process in Health-care environments, using Petri Net formalism, and extract information from those models through simulation, to support the decision making relating human resource availability. This work was done during a stage at the Cartif Foundation in Valladolid Spain, with the cooperation of the Valladolid University‟s School of Industrial Engineering. Este estudo examina o procedimento para distribuição de medicamentos dentro de um hospital, baseado numa pesquisa bibliográfica e uma entrevista com o director da farmácia do hospital “Hospital del Rio Ortega” em Valladolid, Espanha. Foi necessário elaborar um fluxogram teórico do procedimento de distribuição de medicamentos descrevendo os vários passos do processo, e ainda os objectivos do sistema e os seus pontos críticos. Todos estes passos dependem de vários assistentes e auxiliares de saúde directamente ligadas. Esta sistematização permitiu observar os pontos críticos, compreendido como os elementos com impacto critico na qualidade do sistema de distribuição. A compreensão das possíveis causas dos problemas do sistema servem de base para formular questões que tornam possível a sua avaliação. Existem dois sistemas básicos de distribuição de medicamentos: Colectivo e Individual. O sistema colectivo é o tipo de distribuição mais primitivo, mas apesar disso existem muitos hospitais do mundo que adoptam este sistema por ser considerado o mais simples e de implementação mais barata. O sistema individual é mais complexo e necessita de mais profissionais qualificados, nomeadamente farmacêutico e\ou técnico de farmácia, a trabalhar 24 horas por dia, tendo como principal característica o facto de que cada produto ou medicamento é dispensado por pessoa e não por sector ou andar em que um possa estar hospitalizado. A pesquisa de erros médicos devido ao tipo de distribuição de medicamentos adoptado pelos hospitais tem criado debate sobre as vantagens e desvantagens dos sistemas existentes. O uso de um modelo para a distribuição de medicamentos levará á redução de erros e acima de tudo pode contribuir para a redução de custos do hospital. Um dos objectivos deste estudo é mostrar o melhor método de distribuição de medicamentos de uma farmácia hospitalar, isto é, o método de distribuição em que se minimiza o risco de erros de medicação, tempos de distribuição assim como necessidade de recursos humanos. O objectivo principal deste trabalho é modelar o processo de distribuição de medicamentos em ambiente hospitalar, usando o formalismo das Redes de Petri, e extrair informação desses modelos através de simulação para apoiar tomadas de decisão relativas á disponibilidade de recursos humanos. Este trabalho foi desenvolvido durante uma estadia na Fundação Cartif de Valladolid em Espanha com a cooperação da Escola de Engenharias Industriais da Universidade de Valladolid

A pragmatic method for integrated modeling of security attacks and countermeasures

In recent years, research efforts in cyber security have steadily increased as a result of growing concerns for cyber attacks and also increasing trend in cyber attack incidents. One of the important areas of research that is gaining importance is modeling of attacks and countermeasures to quantify survivability and other security measures of interest. In this context, on one extreme, attack trees model has received attention due to its simplicity and ease of analysis, and on the other extreme, stochastic models have been advocated. While attack trees model does not capture complex dependencies among events and also is not amenable for modeling dynamic nature of the attacks and countermeasures, the fitness of stochastic models is yet to be established as there is not sufficient evidence to show that attack and defense behaviors follow some known distributions. With this motivation, a new attack modeling approach based on Petri nets, called PENET, is developed in this thesis whose goal is to significantly enhance the modeling power of attack trees. PENET introduces relevant concepts such as dynamic nature of attack, repairability of a system, and the existence of recurring attacks. Moreover, it attempts to find a balance between ease of use and representation power by providing set of constructs, parameters, performance metrics, and time domain analysis of attack progress. Time domain analysis produces valuable output such as time to reach the main goal and the path taken by the attacker. This output helps to evaluate system survivability and defense strategies. This approach is implemented as a software tool, called PENET Tool, which lets users draw model diagrams of a given system through intuitive user interface, perform time domain simulations and carry out security evaluations, and enable interactive ways to improve the survivability of the system

Model-driven development of data intensive applications over cloud resources

The proliferation of sensors over the last years has generated large amounts of raw data, forming data streams that need to be processed. In many cases, cloud resources are used for such processing, exploiting their flexibility, but these sensor streaming applications often need to support operational and control actions that have real-time and low-latency requirements that go beyond the cost effective and flexible solutions supported by existing cloud frameworks, such as Apache Kafka, Apache Spark Streaming, or Map-Reduce Streams. In this paper, we describe a model-driven and stepwise refinement methodological approach for streaming applications executed over clouds. The central role is assigned to a set of Petri Net models for specifying functional and non-functional requirements. They support model reuse, and a way to combine formal analysis, simulation, and approximate computation of minimal and maximal boundaries of non-functional requirements when the problem is either mathematically or computationally intractable. We show how our proposal can assist developers in their design and implementation decisions from a performance perspective. Our methodology allows to conduct performance analysis: The methodology is intended for all the engineering process stages, and we can (i) analyse how it can be mapped onto cloud resources, and (ii) obtain key performance indicators, including throughput or economic cost, so that developers are assisted in their development tasks and in their decision taking. In order to illustrate our approach, we make use of the pipelined wavefront array

Recent advances in petri nets and concurrency

CEUR Workshop Proceeding